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Eigen::JacobiRotation< Scalar > Class Template Reference
Dense matrix and array manipulation » Reference » Jacobi_Module

Rotation given by a cosine-sine pair. More...

#include <Jacobi.h>

Public Types

typedef NumTraits< Scalar >::Real RealScalar
 

Public Member Functions

EIGEN_DEVICE_FUNC JacobiRotation ()
 
EIGEN_DEVICE_FUNC JacobiRotation (const Scalar &c, const Scalar &s)
 
EIGEN_DEVICE_FUNC Scalar & c ()
 
EIGEN_DEVICE_FUNC Scalar c () const
 
EIGEN_DEVICE_FUNC Scalar & s ()
 
EIGEN_DEVICE_FUNC Scalar s () const
 
EIGEN_DEVICE_FUNC JacobiRotation operator* (const JacobiRotation &other)
 
EIGEN_DEVICE_FUNC JacobiRotation transpose () const
 
EIGEN_DEVICE_FUNC JacobiRotation adjoint () const
 
template<typename Derived >
EIGEN_DEVICE_FUNC bool makeJacobi (const MatrixBase< Derived > &, Index p, Index q)
 
EIGEN_DEVICE_FUNC bool makeJacobi (const RealScalar &x, const Scalar &y, const RealScalar &z)
 
EIGEN_DEVICE_FUNC void makeGivens (const Scalar &p, const Scalar &q, Scalar *r=0)
 

Protected Member Functions

EIGEN_DEVICE_FUNC void makeGivens (const Scalar &p, const Scalar &q, Scalar *r, internal::true_type)
 
EIGEN_DEVICE_FUNC void makeGivens (const Scalar &p, const Scalar &q, Scalar *r, internal::false_type)
 

Protected Attributes

Scalar m_c
 
Scalar m_s
 

Detailed Description

template<typename Scalar>
class Eigen::JacobiRotation< Scalar >

Rotation given by a cosine-sine pair.

\jacobi_module

This class represents a Jacobi or Givens rotation. This is a 2D rotation in the plane J of angle $ \theta $ defined by its cosine c and sine s as follow: $ J = \left ( \begin{array}{cc} c & \overline s \\ -s & \overline c \end{array} \right ) $

You can apply the respective counter-clockwise rotation to a column vector v by applying its adjoint on the left: $ v = J^* v $ that translates to the following Eigen code:

v.applyOnTheLeft(J.adjoint());
v
Array< int, Dynamic, 1 > v
Definition Array_initializer_list_vector_cxx11.cpp:1
J
JacobiRotation< float > J
Definition Jacobi_makeJacobi.cpp:3
See also
MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()

Member Typedef Documentation

◆ RealScalar

template<typename Scalar >
typedef NumTraits<Scalar>::Real Eigen::JacobiRotation< Scalar >::RealScalar

Constructor & Destructor Documentation

◆ JacobiRotation() [1/2]

template<typename Scalar >
EIGEN_DEVICE_FUNC Eigen::JacobiRotation< Scalar >::JacobiRotation ( )
inline

Default constructor without any initialization.

◆ JacobiRotation() [2/2]

template<typename Scalar >
EIGEN_DEVICE_FUNC Eigen::JacobiRotation< Scalar >::JacobiRotation ( const Scalar &  c,
const Scalar &  s 
)
inline

Construct a planar rotation from a cosine-sine pair (c, s).

Member Function Documentation

◆ adjoint()

template<typename Scalar >
EIGEN_DEVICE_FUNC JacobiRotation Eigen::JacobiRotation< Scalar >::adjoint ( ) const
inline

Returns the adjoint transformation

◆ c() [1/2]

template<typename Scalar >
EIGEN_DEVICE_FUNC Scalar & Eigen::JacobiRotation< Scalar >::c ( )
inline

◆ c() [2/2]

template<typename Scalar >
EIGEN_DEVICE_FUNC Scalar Eigen::JacobiRotation< Scalar >::c ( ) const
inline

◆ makeGivens() [1/3]

template<typename Scalar >
EIGEN_DEVICE_FUNC void Eigen::JacobiRotation< Scalar >::makeGivens ( const Scalar &  p,
const Scalar &  q,
Scalar *  r,
internal::false_type   
)
protected

◆ makeGivens() [2/3]

template<typename Scalar >
EIGEN_DEVICE_FUNC void Eigen::JacobiRotation< Scalar >::makeGivens ( const Scalar &  p,
const Scalar &  q,
Scalar *  r,
internal::true_type   
)
protected

◆ makeGivens() [3/3]

template<typename Scalar >
EIGEN_DEVICE_FUNC void Eigen::JacobiRotation< Scalar >::makeGivens ( const Scalar &  p,
const Scalar &  q,
Scalar *  r = 0 
)

Makes *this as a Givens rotation G such that applying $ G^* $ to the left of the vector $ V = \left ( \begin{array}{c} p \\ q \end{array} \right )$ yields: $ G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )$.

The value of r is returned if r is not null (the default is null). Also note that G is built such that the cosine is always real.

Example:

Output: 

This function implements the continuous Givens rotation generation algorithm found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem. LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.


See also
MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight() 








◆ makeJacobi() [1/2]








template<typename Scalar > 



template<typename Derived > 



  

  
      

        

          EIGEN_DEVICE_FUNC bool Eigen::JacobiRotation< Scalar >::makeJacobi 
          (
          const MatrixBase< Derived > & 
          m, 
        

        

          
          
          Index 
          p, 
        

        

          
          
          Index 
          q 
        

        

          
          )
          
        

      

  		
  
inline  
  






Makes *this as a Jacobi rotation J such that applying J on both the right and left sides of the 2x2 selfadjoint matrix $ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )$ yields a diagonal matrix $ A = J^* B J $


Example: 
 Output: 
See also
JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight() 








◆ makeJacobi() [2/2]








template<typename Scalar > 

      

        

          EIGEN_DEVICE_FUNC bool Eigen::JacobiRotation< Scalar >::makeJacobi 
          (
          const RealScalar & 
          x, 
        

        

          
          
          const Scalar & 
          y, 
        

        

          
          
          const RealScalar & 
          z 
        

        

          
          )
          
        

      




Makes *this as a Jacobi rotation J such that applying J on both the right and left sides of the selfadjoint 2x2 matrix $ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )$ yields a diagonal matrix $ A = J^* B J $


See also
MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight() 








◆ operator*()








template<typename Scalar > 



  

  
      

        

          EIGEN_DEVICE_FUNC JacobiRotation Eigen::JacobiRotation< Scalar >::operator* 
          (
          const JacobiRotation< Scalar > & 
          other)
          
        

      

  		
  
inline  
  






Concatenates two planar rotation 








◆ s() [1/2]








template<typename Scalar > 



  

  
      

        

          EIGEN_DEVICE_FUNC Scalar & Eigen::JacobiRotation< Scalar >::s 
          (
          )
          
        

      

  		
  
inline  
  












◆ s() [2/2]








template<typename Scalar > 



  

  
      

        

          EIGEN_DEVICE_FUNC Scalar Eigen::JacobiRotation< Scalar >::s 
          (
          )
           const
        

      

  		
  
inline  
  












◆ transpose()








template<typename Scalar > 



  

  
      

        

          EIGEN_DEVICE_FUNC JacobiRotation Eigen::JacobiRotation< Scalar >::transpose 
          (
          )
           const
        

      

  		
  
inline  
  






Returns the transposed transformation 







Member Data Documentation



◆ m_c








template<typename Scalar > 



  

  
      

        

          Scalar Eigen::JacobiRotation< Scalar >::m_c
        

      

  		
  
protected  
  












◆ m_s








template<typename Scalar > 



  

  
      

        

          Scalar Eigen::JacobiRotation< Scalar >::m_s
        

      

  		
  
protected  
  











The documentation for this class was generated from the following files:





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